Generalized Uncertainty Principle in three-dimensional gravity and the BTZ black hole

Abstract

We investigate the structure of the gravity-induced Generalized Uncertainty Principle in three dimensions. The subtleties of lower dimensional gravity, and its important differences with respect to four and higher dimensions, are duly taken into account, by considering different possible candidates for the gravitational radius, $R_g$, that is the minimal length/maximal resolution of the quantum mechanical localization process. We find that the event horizon of the $M\ne 0$ Bañados-Teitelboim-Zanelli micro black hole furnishes the most consistent $R_g$. This allows us to obtain a suitable formula for the Generalized Uncertainty Principle in three dimensions, and also to estimate the corrections induced by the latter on the Hawking temperature and Bekenstein entropy. We also point to the extremal $M=0$ case, and its natural unit of length introduced by the cosmological constant, $\ell =1/\sqrt{-\Lambda }$, as a possible alternative to $R_g$, and present a condensed matter analog realization of this scenario.

arXiv commentv2: 26 pages, 4 figures, accepted for publication in Phys.Rev.D

References in corpus (64)

• The electronic properties of graphene
• The Large N Limit of Superconformal Field Theories and Supergravity
• The Black Hole in Three Dimensional Space Time
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Geometry of the 2+1 Black Hole
• The holographic principle
• The quantum structure of spacetime at the Planck scale and quantum fields
• Evanescent Black Holes
• A Generalized Uncertainty Principle in Quantum Gravity
• Dirac materials
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The Generalized Uncertainty Principle and Black Hole Remnants
• Generalized Lorentz invariance with an invariant energy scale
• Probing Planck-scale physics with quantum optics
• Dilaton Gravity in Two Dimensions
• On Gravity and the Uncertainty Principle
• A proposal for testing Quantum Gravity in the lab
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• Generalized Uncertainty Principle, Extra-dimensions and Holography
• Gravitational tests of the Generalized Uncertainty Principle
• Will we observe black holes at LHC?
• GUP parameter from quantum corrections to the Newtonian potential
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• Uncertainty Relation on World Crystal and its Applications to Micro Black Holes
• Gravitationally Collapsing Dust in $(2+1)$ Dimensions
• How classical are TeV-scale black holes?
• Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect, and all that
• Dimensionally Reduced Gravitational Chern-Simons Term and its Kink
• Generalized Uncertainty Principle and Corpuscular Gravity
• The Hawking-Unruh phenomenon on graphene
• Modified Unruh effect from Generalized Uncertainty Principle
• Generalized Uncertainty Principle, Black Holes, and White Dwarfs: A Tale of Two Infinities
• Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• Lorentz violation and generalized uncertainty principle
• Testing of Generalized Uncertainty Principle With Macroscopic Mechanical Oscillators and Pendulums
• Graphene and the Zermelo Optical Metric of the BTZ Black Hole
• Horizon wave-function for single localized particles: GUP and quantum black hole decay
• Stellar Equilibrium in 2+1 Dimensions
• Weyl-Gauge Symmetry of Graphene
• GUP parameter from Maximal Acceleration
• Potential tests of the Generalized Uncertainty Principle in the advanced LIGO experiment
• Generalised uncertainty relations from superpositions of geometries
• Curved Spacetimes and Curved Graphene: a status report of the Weyl-symmetry approach
• Generalized uncertainty principles and quantum field theory
• Parallel Transport of Electrons in Graphene Parallels Gravity
• The deformation parameter of the generalized uncertainty principle
• Generalized Dirac structure beyond the linear regime in graphene
• Revisiting the gauge fields of strained graphene
• On the negative spectrum of the 2+1 black hole
• Holographic entanglement entropy of the BTZ black hole
• Glimpses on the micro black hole Planck phase
• Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter black holes
• On the Space-Time Symmetries of Non-Commutative Gauge Theories
• Using Weyl symmetry to make Graphene a real lab for fundamental physics
• (Anti-)de Sitter, Poincaré, Super symmetries, and the two Dirac points of graphene
• Torsion in quantum field theory through time-loops on Dirac materials
• Special Relativity induced by Granular Space
• Graphene: QFT in curved spacetimes close to experiments
• Indirect Probe of Quantum Gravity using Molecular Wave-packets
• Generalized uncertainty principle in graphene
• Gauged WZW models for space-time groups and gravitational actions
• Hawking temperature for various kinds of black holes from Heisenberg uncertainty principle

Cited by in corpus (31)

• Phenomenology of GUP stars
• Baryon Asymmetry from the Generalized Uncertainty Principle
• Non-Pertubative Quantum Corrections to a Born-Infeld Black Hole and its Information Geometry
• PV criticality of Achucarro-Ortiz black hole in the presence of higher order quantum and GUP corrections
• Exponential corrected thermodynamics of black holes
• Effect of the modified Heisenberg algebra on the Black hole thermodynamics
• Thermodynamics and Shadows of quantum-corrected Reissner-Nordström black hole surrounded by quintessence
• Hunting Quantum Gravity with Analogs: the case of graphene
• The generalized uncertainty principle effect in acoustic black holes
• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity
• Non-perturbative correction to the Horava-Lifshitz black hole thermodynamics
• Gravitational effects on the Heisenberg Uncertainty Principle: a geometric approach
• Quantum corrections to the thermodynamics of rotating charged BTZ black hole in gravity's rainbow
• Torsion at different scales: from materials to the Universe
• Higher-order generalized uncertainty principle applied to gravitational baryogenesis
• Higher-order generalized uncertainty principle corrections to the Jeans mass
• The three "layers" of graphene monolayer and their analog generalized uncertainty principles
• On the Chandrasekhar Limit in Generalized Uncertainty Principles
• Turning graphene into a lab for noncommutativity
• The generalized uncertainty principle impact onto the black hole thermodynamic phase transition
• Exotic fermionic fields and minimal length
• Microstructure of Charged AdS Black Hole with Minimal Length Effects
• The new higher-order generalized uncertainty principle and primordial big bang nucleosynthesis
• The gravitational baryogenesis and a new higher-order extended uncertainty principle with parameter adaptability for the minimum length
• Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds
• Time-loops to spot torsion on bidimensional Dirac materials with dislocations
• Exploring non-perturbative effects on quasi-topological black hole thermodynamics
• Remarks on SU_q(2) fermions
• Phenomenology of Schwarzschild-like Black Holes with a Generalized Compton Wavelength
• Low Energy Consequences of Loop Quantum Gravity
• Minimal length implications on the Hartree-Fock theory